Letπ:(X,T)→(Y,S)be a factor map between two topological dynamical systems,and F_(a) Furstenberg family of Z.We introduce the notion of relative broken F-sensitivity.Let Fs(resp.Fpubd,Finf)be the families consisting ...Letπ:(X,T)→(Y,S)be a factor map between two topological dynamical systems,and F_(a) Furstenberg family of Z.We introduce the notion of relative broken F-sensitivity.Let Fs(resp.Fpubd,Finf)be the families consisting of all syndetic subsets(resp.positive upper Banach density subsets,infinite subsets).We show that for a factor mapπ:(X,T)→(Y,S)between transitive systems,πis relatively broken F-sensitive for F=Fs or Fpubd if and only if there exists a relative sensitive pair which is an F-recurrent point of(R_(π),T^((2)));is relatively broken Finf-sensitive if and only if there exists a relative sensitive pair which is not asymptotic.For a factor mapπ:(X,T)→(Y,S)between minimal systems,we get the structure of relative broken F-sensitivity by the factor map to its maximal equicontinuous factor.展开更多
基金Supported by NNSF of China(Grant Nos.12001354,12171298)。
文摘Letπ:(X,T)→(Y,S)be a factor map between two topological dynamical systems,and F_(a) Furstenberg family of Z.We introduce the notion of relative broken F-sensitivity.Let Fs(resp.Fpubd,Finf)be the families consisting of all syndetic subsets(resp.positive upper Banach density subsets,infinite subsets).We show that for a factor mapπ:(X,T)→(Y,S)between transitive systems,πis relatively broken F-sensitive for F=Fs or Fpubd if and only if there exists a relative sensitive pair which is an F-recurrent point of(R_(π),T^((2)));is relatively broken Finf-sensitive if and only if there exists a relative sensitive pair which is not asymptotic.For a factor mapπ:(X,T)→(Y,S)between minimal systems,we get the structure of relative broken F-sensitivity by the factor map to its maximal equicontinuous factor.
